Many scientific and medical monitoring systems generate multivariate and longitudinal data. The term “multivariate” means that the monitoring system obtains data for multiple, dependent, variables for each subject of interest to the system. The term “longitudinal” means that the data is obtained for the multiple variables at multiple times during the monitoring process. One common example of a multivariate and longitudinal monitoring system is a patient health monitoring system. The patient health monitoring system monitors various attributes associated with the health of a patient, such as heart rate, blood pressure, blood sugar, temperature, weight, respiration, disease symptoms, and the like. The data for the attributes or variables associated with the patient may differ at the sample times so the system is a longitudinal data system, and the health monitoring system is multivariate because the monitoring system collects variable data corresponding to two or more attributes. A monitoring system can include an automated device that measures and collects the medical data for the multiple variables over time. Alternatively, the medical data can be collected during a series of medical exams performed by a healthcare provider.
A health care provider can diagnose various medical conditions and monitor the course of medical treatment over time using the multivariate longitudinal medical data. The medical data can, however, be partially incomplete at various times. For example, a set of medical data can include variables corresponding to respiration rate, heart rate, and temperature of a patient that are monitored over time. In some instances, at least one of the variables is not recorded at the same time as the other variables. For example, the heart rate and temperature of the patient are recorded one day, and the respiration rate and heart rate are measured on another day. Both sets of medical data are partially complete for the patient. Various methods exist for handling incomplete data sets, but all of the existing methods have limitations. One method of handling the missing data is to simply ignore medical records that are only partially complete, but this also ignores valuable medical data. Other methods, generally denoted as correlation methods, use a predetermined correlation model to estimate a value for the variable not sampled using the known values for the sampled variables. Correlation methods can suffer from bias and the correlation models are based on a large group of patients that may not represent an individual patient accurately. Still other methods include time based regression techniques that impute a value for the missing data based on medical data for the patient from other times. While the regression techniques can be useful in some cases, the regression techniques tend to generate values that correspond to a long-term average of a medical attribute and can ignore potential short term changes in the condition of the patient.
Patient health monitoring systems have a wide variety of uses in providing medical care to patients and monitoring chronic conditions. Some patient monitoring systems are used in the field of telemedicine and home health care. In a telemedicine system, a patient is geographically removed from the presence of a doctor or other healthcare provider. For example, the patient could be at home instead of on site at a healthcare facility. One or more telemedical devices enable the healthcare provider to monitor the health status of a patient and potentially diagnose and treat some medical problems without the need for the patient to travel to the healthcare facility. The use of telemedical systems has the potential to reduce the cost of healthcare, and to improve the quality of healthcare through increased patient monitoring.
While telemedicine systems have numerous advantages, one disadvantage relates to the aforementioned problem of missing medical data. While any medical monitoring system can generate incomplete medical data, the telemedical systems are more prone to missing data at various times since such systems rely on the patient to operate a monitoring device or provide medical information. In some instances, a partial set of medical data is generated at a given time while the data corresponding to one or more attributes are missing. For example, a patient in a telemedicine system may remember to check his blood pressure but forget to check his blood sugar level on a given day. As described above, existing systems and methods for handling missing medical data have limitations that present challenges to medical and scientific study of the partial data. Consequently, improvements to the analysis of partially complete multivariate longitudinal data would be beneficial.